Another critical aspect of the temporal behaviour of black hole X-ray binaries is that typically, the systems show hard lags such that the high energy photons are delayed relative to the soft ones. The time-lags increase logarithmically with energy and are surprisingly frequency dependent, \(t_{lag} \propto f^{-0.7}\)  [1]}, [2]}, [3]}. The magnitude of these lags are too large for them to be due to light crossing time-scales or due to Comptonization unless the corona is unphysically larger than \(10^{9}\)  cms [4]}, [5]}. Instead, the propagation model provides an interpretation where if softer photons are produced at a larger radii compared to the high energy ones, there will be a time-lag between them corresponding to the time take for the fluctuation to propagate from the outer radius to the inner regions [6]}, [7]}. The energy and frequency dependence of these time-lags can also be explained within such a framework [6]}, [7]}. For many years, it has been puzzling why high accretion rate systems do not seem to be affected strongly by the radiation pressure instability [10]}, [11]}. The instability should have made bright black hole X-ray binaries in their soft state (when they are supposed to have a standard accretion disc) to have X-ray flux variations of several orders of magnitude over time-scales of minutes. Interestingly, the absence of such variation could be due viscous fluctuations in the disc [12]}.
